# Matrix Multiplication Calculator

## Multiply matrices step by step

The calculator will find the product of two matrices (if possible), with steps shown. It multiplies matrices of any size up to 10x10 (2x2, 3x3, 4x4 etc.).

Related calculator: Matrix Calculator

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If the calculator did not compute something or you have identified an error, or you have a suggestion/feedback, please write it in the comments below.

The Matrix Multiplication Calculator offers you a quick and straightforward way to multiply matrices, saving you time and effort. It's not only about speed but also accuracy. With our advanced computational algorithms, you can rest assured that the results are not only quickly delivered but also correct. Accuracy is our watchword, and every calculation run on this platform adheres to this principle.

## How to Use the Matrix Multiplication Calculator?

• ### Input the First Matrix

Begin by entering the elements of the first matrix. You will find fields corresponding to its rows and columns. Make sure you enter the elements according to its actual dimensions. For instance, if your first matrix is 2x3, there should be two rows and three columns filled in.

• ### Enter the Second Matrix

Now, enter the elements of the second matrix. It's critical to note that the number of rows in this second one should match the number of columns in the first one. This is because, in matrix multiplication, each element in the first matrix's row must pair with a corresponding element in the second matrix's column.

• ### Click "Calculate"

Once you have entered both matrices accurately, click the "Calculate" button. The calculator will swiftly perform the matrix multiplication and display the result.

• ### Review the Result

After the calculator completes the multiplication, you will see the resultant matrix, often referred to as matrix $C$. This new matrix is the product of the multiplication of the first matrix and the second matrix.

## What Is Matrix Multiplication?

Matrix multiplication involves combining two matrices to generate a new matrix. Unlike regular multiplication, it involves the sum of the products of corresponding elements from rows of the first matrix and columns of the second one. The mathematical formula for matrix multiplication, given a $m\times n$ matrix $A=\left[a_{ij}\right]$ and a $n\times k$ matrix $B=\left[b_{ij}\right]$, is as follows:

$$c_{ij}=\sum_{s=1}^n a_{is}b_{sj}$$

Here, $c_{ij}$ is the element of the new matrix, matrix $C$, resulting from the multiplication.

## Sample Matrix Multiplication

Consider two matrices, $A$ and $B$, where $A$ is a 2x3 matrix and $B$ is a 3x2 matrix.

Matrix $A=\left[\begin{array}{ccc}1&2&3\\4&5&6\end{array}\right]$.

Matrix $B=\left[\begin{array}{cc}7&8\\9&10\\11&12\end{array}\right]$.

By multiplying these two matrices, we get:

$$C=AB=\left[\begin{array}{ccc}1&2&3\\4&5&6\end{array}\right]\left[\begin{array}{cc}7&8\\9&10\\11&12\end{array}\right]=\left[\begin{array}{cc}1\cdot 7+2\cdot 9+3\cdot 11&1\cdot 8+2\cdot 10+3\cdot 12\\4\cdot 7+5\cdot 9+6\cdot 11&4\cdot 8+5\cdot 10+6\cdot 12\end{array}\right]=\left[\begin{array}{cc}58&64\\139&154\end{array}\right]$$

## Why Choose Our Matrix Multiplication Calculator?

• ### High Accuracy

Our calculator utilizes advanced algorithms to deliver highly accurate results. You can trust that the output is correct and precise.

• ### Speed and Efficiency

The calculator is designed for speed. It quickly performs matrix multiplication, saving you time and reducing the chance of errors that can occur with manual calculations.

• ### Versatility

Our calculator can handle various dimensions for matrices, catering to a wide range of mathematical problems and scenarios. Whether you are working with a 2x2 or a 5x5 matrix, our calculator has got you covered.

• ### Free Access

You can use our calculator for free, making it a cost-effective tool for students, teachers, and professionals.

• ### Educational Tool

Besides providing the multiplication result, our calculator also helps users understand the process of matrix multiplication. It's a great educational tool for those learning linear algebra or any field where matrix multiplication is used.

### FAQ

#### I made an error entering my matrices. How can I correct this?

Simply clear the fields and re-enter the correct matrices. Then, click "Calculate" again to get the new result.

#### Can I access the Matrix Multiplication Calculator from my mobile device?

Yes, our Matrix Multiplication Calculator is designed to be accessible from any device with an internet connection, including smartphones and tablets.

#### How accurate is the Matrix Multiplication Calculator?

Our calculator uses advanced computational algorithms to ensure high accuracy in results. You can trust it to provide correct results for your matrix multiplication tasks.

#### Can I use the calculator for matrices of any size?

Our Matrix Multiplication Calculator can handle matrices of any size up to 10x10. However, remember that, in matrix multiplication, the number of columns in the first matrix must equal the number of rows in the second matrix.